Applicability of Time Average Stochastic Moire for Cryptographic Applications

Abstract

An algorithm for the construction of Hash function [1] based on optical time average moiré experimental technique is proposed in this paper. Algebraic structures of greyscale colour intensity functions and time average operators are constructed. Properties of time average operators and effects of digital image representation are explored. The fact that the inverse problem of identification of the original greyscale colour intensity function from its time averaged image is an ill-posed problem and is computationally infeasible helps to construct an efficient algorithm for the construction of one-way Hash function applicable in cryptographic algorithms.

Inverse problems involving time average geometric moiré [2] are characterized by the fact that the information of interest (e.g. the distribution of greyscale colour intensity on the surface of a non-deformable body) is not directly available. The imaging device (the camera) provides measurements of a transformation of this information in the process of time averaging while the body performs complex chaotic in-plane motion. In practice, these measurements are both incomplete (sampling) and inaccurate (statistical noise). This means that one must give up recovering the exact image. Indeed, aiming for full recovery of the information usually results in unstable solutions due to the fact that the reconstructed image is very sensitive to inevitable measurement error. Otherwise expressed, slightly different data would have produced a significantly different image. In order to cope with these difficulties, the reconstructed image is usually defined as the solution of an optimization problem. Solution of the inverse problem from the time average image is known is computationally infeasible and that fact is the object of this study.